Hierarchical and Incremental Multivariate Analysis for Process Control

ABSTRACT

A technique for analyzing two or more data streams respectively generated from two or more components of a controllable process includes the following steps. In a first step, a statistical analysis is performed on each of the two or more data streams to generate first analysis results in the form of respective statistical results for the two or more data streams. In a second step, at least a portion of the statistical results from at least one of the two or more data streams is combined with at least a portion of the statistical results from at least another one of the two or more data streams to yield second analysis results. The controllable process is adjustable based on at least one of the first analysis results and the second analysis results.

FIELD OF THE INVENTION

The present invention relates to process control and, more particularly,to hierarchical and incremental multivariate analysis for use in suchprocess control.

BACKGROUND OF THE INVENTION

In the semiconductor manufacturing process environment, there areseveral different distributed data monitors used to gather information(typically in the form of data streams) about different steps in themanufacturing process, tool operation, wafer defects, test results, etc.Significant improvements in the performance of this manufacturingprocess are achieved by appropriately analyzing the available streamsusing statistical techniques, and using this to drive process control.

There has been a large amount of work on developing the appropriatestatistical analytic solutions for different kinds of gathered data. Animportant statistical process control (SPC) method uses multivariateanalysis on the time series and thresholds the resulting summarystatistics to detect out-of-specification tool parameters, and uses thisto control the tool operation. However, most of these schemes performanalysis on data gathered from one tool, i.e., analysis is performed ona data stream from one tool at a time. This leads to limitations in theSPC performance, as it deters cross-tool, cross-step, andcross-data-source analysis.

SUMMARY OF THE INVENTION

Principles of the invention provide hierarchical and incrementalstatistical analysis for use in such process control.

By way of example, in a first aspect of the invention, a method foranalyzing two or more data streams respectively generated from two ormore components of a controllable process comprises the following steps.In a first step, a statistical analysis is performed on each of the twoor more data streams to generate first analysis results in the form ofrespective statistical results for the two or more data streams. In asecond step, at least a portion of the statistical results from at leastone of the two or more data streams is combined with at least a portionof the statistical results from at least another one of the two or moredata streams to yield second analysis results. The controllable processis adjustable based on at least one of the first analysis results andthe second analysis results.

The statistical analysis may comprise a multivariate analysis. The firstanalysis results may comprise incremental summary statistics for each ofthe two or more data streams. The second analysis results may comprisehierarchical summary statistics for the two or more data streams. Thehierarchical summary statistics for the two or more data streams may becomputed using a decision tree classifier. The decision tree may beusable to adjust one or more components of the controllable process. Inone embodiment, the controllable process comprises a semiconductormanufacturing process, e.g., a silicon wafer manufacturing process.

In a second aspect of the invention, an article of manufacture foranalyzing two or more data streams respectively generated from two ormore components of a controllable process comprises a computer readablestorage medium including one or more programs which when executed by acomputer perform the above described first (intermediate analysis) andsecond (hierarchical analysis) steps.

In a third aspect of the invention, apparatus for analyzing two or moredata streams respectively generated from two or more components of acontrollable process comprises: a memory; and a processor coupled to thememory and operative to: (i) perform a statistical analysis on each ofthe two or more data streams to generate first analysis results in theform of respective statistical results for the two or more data streams;and (ii) combine at least a portion of the statistical results from atleast one of the two or more data streams with at least a portion of thestatistical results from at least another one of the two or more datastreams to yield second analysis results; wherein the controllableprocess is adjustable based on at least one of the first analysisresults and the second analysis results.

In a fourth aspect of the invention, a system for analyzing two or moredata streams respectively generated from two or more tools of asemiconductor processing pipeline comprises the following elements. Adata storage unit stores the two or more data streams. A statisticalanalyzer is coupled to the data storage unit and operative to: (i)perform a multivariate analysis on each of the two or more data streamsto generate first analysis results in the form of respective statisticalresults for the two or more data streams; and (ii) combine at least aportion of the statistical results from at least one of the two or moredata streams with at least a portion of the statistical results from atleast another one of the two or more data streams to yield secondanalysis results; wherein at least a portion of the two or more tools ofthe semiconductor processing pipeline is adjustable based on at leastone of the first analysis results and the second analysis results.

These and other objects, features and advantages of the presentinvention will become apparent from the following detailed descriptionof illustrative embodiments thereof, which is to be read in connectionwith the accompanying drawings.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 illustrates a hierarchical and incremental multivariate analysissystem according to an embodiment of the invention.

FIG. 2 illustrates a methodology for hierarchical and incrementalmultivariate analysis according to an embodiment of the invention.

FIG. 3 illustrates a hierarchical and incremental multivariate analysissystem for a chemical mechanical polishing (CMP) tool according to anembodiment of the invention.

FIG. 4 illustrates a decision tree formed by a hierarchical analysisprocess according to an embodiment of the invention.

FIG. 5 illustrates a confusion matrix for a two class classificationaccording to an embodiment of the invention.

FIG. 6 illustrates a computer system wherein techniques for performinghierarchical and incremental multivariate analysis may be implementedaccording to an embodiment of the invention.

DETAILED DESCRIPTION OF PREFERRED EMBODIMENTS

Illustrative embodiments of the invention will be described below in thecontext of statistical process control (SPC) in a semiconductormanufacturing process. However, it is to be understood that theprinciples of the invention are not limited thereto and may be used inapplications other than a semiconductor manufacturing process. It shouldalso be understood that the invention is not limited to the particularmaterials, features, processing steps, and applications shown anddescribed herein.

In order to improve performance of the SPC and, in the context of theillustrative semiconductor processing embodiment, the resulting waferyield, we propose to perform multivariate analysis across several of theavailable data streams to identify cross-tool, cross-step andcross-process dependencies that cannot be captured by the limitedanalysis of current SPC techniques. In order to deal with the potentiallarge data volume, we propose to use an incremental and hierarchicalstatistical analysis approach.

In our proposed approach, small groups of data streams are firststatistically analyzed to create intermediate summary statistics (eachof which may be independently used for analysis and process control).These intermediate summary statistics are aggregated across several datastreams and analyzed using other (potentially similar) statisticaltechniques to obtain more comprehensive results. Computation savingsarise from this hierarchical evaluation, where results are reused acrossdifferent time-scales, and groups of data streams, allowing large-scaleanalysis across many different tools, steps and processes.

At the same time, in order to drive real-time operation, theintermediate results included in these summary statistics may alsoindividually be used to drive process control incrementally. Refinementsto any control decision (made by this independent analysis) may beprovided after the hierarchical analysis. Note that the granularity ofthis hierarchical analysis can be at multiple levels.

FIG. 1 illustrates hierarchical and incremental multivariate analysissystem according to an embodiment of the invention. As may be seen inFIG. 1, in accordance with system 100, there are two tools 102-1 (tool1) and 102-2 (tool 2) which produce N and M data streams, respectively.Of course, there could be more or less tools. Each data stream may beanalyzed using multivariate analysis (intermediate analyzers 104) tocreate summary statistics S₁ ¹ through S_(N) ¹ and S₁ ² through S_(M) ²,respectively.

These summary statistics may be used to drive process control 106 assoon as they are computed (this leads to incremental process control,i.e., we do not have to wait for all the analysis to complete).Additionally, these summary statistics may also be analyzed in ahierarchical structure with multiple levels (hierarchical analyzers 108)to generate new results which may then be also used to drive the processcontrol 106. Finally, there may also be other data streams such asmeasurement data that may be used in this hierarchical analysis.

Based on results from the analyzers, individual and multiple aspects(components) of the processing pipeline (tools) can be controlled (e.g.,adjusted) to improve performance (e.g., in a semiconductor manufacturingpipeline, increased wafer yield).

Thus, advantageously, multiple data streams are collected in theenvironment (e.g., a semiconductor manufacturing pipeline). Each datastream is analyzed to generate summary statistics. These summarystatistics are then aggregated across the different streams in ahierarchical manner to generate new analysis results. The processcontrol is incremental. This means that we use not just the results ofthe hierarchical analysis for the process control, instead we also mayuse the intermediate summary statistics (generated per stream) forprocess control. Hence, as and when any analysis results are available,they may be used for the control.

FIG. 2 illustrates a hierarchical and incremental analysis methodologyaccording to an embodiment of the invention. It is to be understood thatmethodology 200 shown in FIG. 2 is performed by system 100 of FIG. 1.

Methodology 200 performs two stages analysis stages.

In step 202 (first stage), methodology 200 performs multivariateanalysis on each data stream associated with a tool to generateintermediate multivariate results. By way of example, respective rawtool parameter traces (i.e., a trace for SiCOH processing tool, a tracefor annealing tool, a trace for chemical mechanical polishing or CMPtool, an example of which will be described below in the context of FIG.3) are each analyzed using a multivariate statistical technique.

By way of one example, the multivariate statistical technique computesmultiple Hoteling-T2 summary statistics per data stream. In oneembodiment, this may include 12 statistical components for a CMP tool,that are partitioned into six fixed components and six variablecomponents. These 12 components are partitioned into six fixedcomponents and six variable components. The fixed components capturesummary statistics for slowly varying parameters, while the variablecomponents capture the summary statistics of rapidly varying parameters.The six sets correspond to the six recipe steps within the tool.

Threshold values are set to indicate parameter out-of-specificationconditions. If the generated Hoteling-T2 scores lie outside thesethreshold values, alarms are generated (incremental resultsutilization). The results of this stage can lead to approximately 10%accurate prediction of wafer yield class (especially to predict waferswith bad yield).

It is to be understood that the multivariate statistical technique thatis used on each data stream (tool) in order to generate a set of summarystatistics can be any conventional multivariate analysis technique. Byway of further example, one or more multivariate analysis techniquesdescribed in U.S. Pat. Nos. 6,442,445; 6,584,368; and 6,678,569, thedisclosures of which are incorporated by reference, may be employed instep 202.

In step 204 (second stage), methodology 200 generates hierarchicalmultivariate results. That is, by way of example, methodology 200 cancombine the time series of summary statistics (12 values per time unit,i.e., per wafer) for the CMP tool with process parameters such as padhours and dresser hours, and builds a decision tree to analyze this datajointly.

Lastly, as shown, step 206 indicates that intermediate results (fromstep 202) and/or the hierarchical results (step 204) can be used toadjust the processing pipeline. Then, steps 202 through 206 can beiterated until some optimum pipeline status is achieved.

FIG. 3 illustrates an embodiment of the invention in the context ofhierarchical and incremental analysis for a CMP tool in the context ofsemiconductor processing pipeline 302. The first multivariate analysis310 operates on the CMP tool trace data stream to create fault detectionand classification (FDC) summary statistics. These FDC summarystatistics are used for process control 312 in existing implementationsby comparing each computed statistic against a fixed threshold. If anyof the summary statistics exceed the threshold, the tool is assumed tobe operating out-of-specification and an alarm is generated. Thisclassification method has accuracy 10%. However, in accordance withprinciples of the invention, hierarchical analysis 314 advantageouslycombines these summary statistics with the process data and uses adecision tree based classifier to build a model to predict bad wafers.

The resulting decision tree is shown in FIG. 4. The construction of thedecision tree follows well-known classification techniques, e.g., asdescribed in P. Domingos and G. Hulten, “Mining High-Speed DataStreams,” ACM SIGKDD 2000, the disclosure of which is incorporated byreference herein. Numerical results corresponding to the classificationaccuracy are shown in FIG. 5.

As shown in exemplary decision tree 400 of FIG. 4, it is assumed thatthe same number of wafers (29) is selected from each class. Then,through 10-fold training and validation, classification performance isevaluated with this decision tree. Each node in the tree corresponds toa decision rule (e.g., is fixed component 4<1.38 at the root) with Ficorresponding to fixed component i and Vj corresponding to variablecomponent j. The results of this second stage in terms of predictingwafer yield class are shown in table of FIG. 5. Confusion matrix 500shows that this classifier achieves nearly 90% accuracy in terms ofclassifying the wafers into these two classes.

Using this hierarchical analysis, we can boost wafer yield predictionresults from about 10% to around 90% achieving significant gains inperformance. Note that we can perform this second stage analysis in acomputationally feasible way because of the preliminary analysis alreadyperformed in the first stage (to generate the Hoteling-T2 summarystatistics). Also note that the results are generated incrementally,i.e., the results of the first stage may already be used to predictwafers with bad yield (although with a low accuracy), while thosegenerated after the second stage of the analysis may be used to refinethose results. It is to be appreciated that the individual techniquesused in this illustrative embodiment, i.e., Hoteling-T2 and decisiontrees, are generic statistical processing techniques, and may bereplaced with other techniques depending on the process beingcontrolled.

Referring lastly to FIG. 6, a computer system is illustrated whereintechniques for performing hierarchical and incremental multivariateanalysis may be implemented according to an embodiment of the invention.That is, FIG. 6 illustrates a computer system in accordance with whichone or more components/steps of the hierarchical and incrementalmultivariate analysis techniques (e.g., components and methodologiesdescribed above in the context of FIGS. 1 through 5) may be implemented,according to an embodiment of the invention. It is to be understood thatthe individual components/steps may be implemented on one such computersystem or on more than one such computer system. In the case of animplementation on a distributed computing system, the individualcomputer systems and/or devices may be connected via a suitable network,e.g., the Internet or World Wide Web. However, the system may berealized via private or local networks. In any case, the invention isnot limited to any particular network.

Thus, the computer system shown in FIG. 6 may represent intermediateanalyzers 104, incremental process control 106 and hierarchicalanalyzers 108, described herein in the context of FIG. 1.

As shown, computer system 600 includes processor 602, memory 604,input/output (I/O) devices 606, and network interface 608, coupled via acomputer bus 610 or alternate connection arrangement.

It is to be appreciated that the term “processor” as used herein isintended to include any processing device, such as, for example, onethat includes a CPU and/or other processing circuitry. It is also to beunderstood that the term “processor” may refer to more than oneprocessing device and that various elements associated with a processingdevice may be shared by other processing devices.

The term “memory” as used herein is intended to include memoryassociated with a processor or CPU, such as, for example, RAM, ROM, afixed memory device (e.g., hard drive), a removable memory device (e.g.,diskette), flash memory, etc. The memory may be considered a computerreadable storage medium.

In addition, the phrase “input/output devices” or “I/O devices” as usedherein is intended to include, for example, one or more input devices(e.g., keyboard, mouse, etc.) for entering data to the processing unit,and/or one or more output devices (e.g., display, etc.) for presentingresults associated with the processing unit.

Still further, the phrase “network interface” as used herein is intendedto include, for example, one or more transceivers to permit the computersystem to communicate with another computer system via an appropriatecommunications protocol.

Accordingly, software components including instructions or code forperforming the methodologies described herein may be stored in one ormore of the associated memory devices (e.g., ROM, fixed or removablememory) and, when ready to be utilized, loaded in part or in whole(e.g., into RAM) and executed by a CPU.

In any case, it is to be appreciated that the techniques of theinvention, described herein and shown in the appended figures, may beimplemented in various forms of hardware, software, or combinationsthereof, e.g., one or more operatively programmed general purposedigital computers with associated memory, implementation-specificintegrated circuit(s), functional circuitry, etc. Given the techniquesof the invention provided herein, one of ordinary skill in the art willbe able to contemplate other implementations of the techniques of theinvention.

Although illustrative embodiments of the present invention have beendescribed herein with reference to the accompanying drawings, it is tobe understood that the invention is not limited to those preciseembodiments, and that various other changes and modifications may bemade by one skilled in the art without departing from the scope orspirit of the invention.

1. A method for analyzing two or more data streams respectivelygenerated from two or more components of a controllable process, themethod comprising the steps of: performing a statistical analysis oneach of the two or more data streams to generate first analysis resultsin the form of respective statistical results for the two or more datastreams; and combining at least a portion of the statistical resultsfrom at least one of the two or more data streams with at least aportion of the statistical results from at least another one of the twoor more data streams to yield second analysis results; wherein thecontrollable process is adjustable based on at least one of the firstanalysis results and the second analysis results.
 2. The method of claim1, wherein the first analysis results comprise incremental summarystatistics for each of the two or more data streams.
 3. The method ofclaim 1, wherein the second analysis results comprise hierarchicalsummary statistics for the two or more data streams.
 4. The method ofclaim 3, wherein the hierarchical summary statistics for the two or moredata streams are computed using a decision tree classifier.
 5. Themethod of claim 4, wherein the decision tree is usable to adjust one ormore components of the controllable process.
 6. The method of claim 1,wherein the controllable process comprises a semiconductor manufacturingprocess.
 7. The method of claim 6, wherein the semiconductormanufacturing process comprises a silicon wafer manufacturing process.8. The method of claim 1, wherein the statistical analysis comprises amultivariate analysis.
 9. An article of manufacture for analyzing two ormore data streams respectively generated from two or more components ofa controllable process, the article comprising a computer readablestorage medium including one or more programs which when executed by acomputer perform the steps of claim
 1. 10. Apparatus for analyzing twoor more data streams respectively generated from two or more componentsof a controllable process, the apparatus comprising: a memory; and aprocessor coupled to the memory and operative to: (i) perform astatistical analysis on each of the two or more data streams to generatefirst analysis results in the form of respective statistical results forthe two or more data streams; and (ii) combine at least a portion of thestatistical results from at least one of the two or more data streamswith at least a portion of the statistical results from at least anotherone of the two or more data streams to yield second analysis results;wherein the controllable process is adjustable based on at least one ofthe first analysis results and the second analysis results.
 11. Theapparatus of claim 10, wherein the first analysis results compriseincremental summary statistics for each of the two or more data streams.12. The apparatus of claim 10, wherein the second analysis resultscomprise hierarchical summary statistics for the two or more datastreams.
 13. The apparatus of claim 12, wherein the hierarchical summarystatistics for the two or more data streams are computed using adecision tree classifier.
 14. The apparatus of claim 13, wherein thedecision tree is usable to adjust one or more components of thecontrollable process.
 15. The apparatus of claim 10, wherein thecontrollable process comprises a semiconductor manufacturing process.16. The apparatus of claim 15, wherein the semiconductor manufacturingprocess comprises a silicon wafer manufacturing process.
 17. Theapparatus of claim 10, wherein the statistical analysis comprises amultivariate analysis.
 18. A system for analyzing two or more datastreams respectively generated from two or more tools of a semiconductorprocessing pipeline, the system comprising: a data storage unit forstoring the two or more data streams; and a statistical analyzer coupledto the data storage unit and operative to: (i) perform a multivariateanalysis on each of the two or more data streams to generate firstanalysis results in the form of respective statistical results for thetwo or more data streams; and (ii) combine at least a portion of thestatistical results from at least one of the two or more data streamswith at least a portion of the statistical results from at least anotherone of the two or more data streams to yield second analysis results;wherein at least a portion of the two or more tools of the semiconductorprocessing pipeline is adjustable based on at least one of the firstanalysis results and the second analysis results.
 19. The system ofclaim 17, wherein the first analysis results comprise incrementalsummary statistics for each of the two or more data streams.
 20. Thesystem of claim 17, wherein the second analysis results comprisehierarchical summary statistics for the two or more data streams.